MPS Calculator (marginal propensity to save & multiplier)

Understanding the marginal propensity to save (MPS) calculator — concept and principle

The marginal propensity to save (MPS) is the share of an extra unit of disposable income that is saved rather than spent. This calculator finds MPS from two observations of income and saving and shows the matching MPC, the simple spending multiplier and the average propensity to save.

Saving rises by $1,500 of the $5,000 increase; the average saving rate also rises from 12% to 13.6%.

How it is calculated

MPS = ΔS ÷ ΔYd, the change in saving divided by the change in disposable income.
MPC = 1 − MPS.
Simple spending multiplier = 1 ÷ MPS.
Average propensity to save APS = S ÷ Y, before and after.

The principle

Disposable income has only two uses: consumption and saving. Any increase must therefore be split between them, so MPC + MPS = 1. In the simple Keynesian model, saving is a leakage from the flow of spending: the more of each extra unit is saved, the less is passed on as someone else's income. That is why the multiplier equals 1 ÷ MPS. APS can even be negative when a household spends more than its income by borrowing or drawing on savings.

Worked example

Default inputs: income 50,000 → 55,000 USD; saving 6,000 → 7,500 USD.

ΔS = 7,500 − 6,000 = 1,500 USD; ΔY = 5,000 USD.
MPS = 1,500 ÷ 5,000 = 0.3.
MPC = 1 − 0.3 = 0.7.
Multiplier = 1 ÷ 0.3 ≈ 3.33.
APS before = 6,000 ÷ 50,000 = 0.12; after = 7,500 ÷ 55,000 ≈ 0.136.

Each point is the calculator re-run with only “Saving after” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Saving after	Marginal propensity to save (MPS)
1,875	-0.825
3,750	-0.45
5,625	-0.075
7,500	0.3
9,375	0.675
11,250	1.05
15,000	1.8

How to read the result

A higher MPS means households save more of any raise. This supports investment over the long run, but in the short run it weakens the multiplier effect of new spending, the so-called paradox of thrift. APS rising with income, as in the example, is common because higher-income households save a larger share.

Common mistakes

Mixing MPS (a change) with APS (a level).
Using gross income rather than disposable income.
Ignoring that saving can fall when income rises if expectations change.
Treating the simple multiplier as the real effect of fiscal policy.

Keep in mind: A simplified textbook relationship. Real saving behaviour depends on interest rates, wealth, expectations and age. For learning, not advice.

Frequently asked questions

What is the relationship between MPC and MPS?

They add up to 1, because extra disposable income is either consumed or saved.

What is the paradox of thrift?

If everyone tries to save more at once, spending and income fall, so total saving may not rise.

How is MPS different from the household saving rate?

The saving rate is an average (APS); MPS is about how saving changes when income changes.

Sources: Keynes, J. M. (1936). The General Theory of Employment, Interest and Money · Samuelson, P. A. & Nordhaus, W. D., Economics (consumption and saving functions)

Checked 9 Nov 2026. BYU–Idaho ECON 151 web text, Lesson 6 “Basic Macroeconomic Relationships” (MPS = ΔS ÷ ΔYd, APS = S ÷ Yd, MPC + MPS = 1); OpenStax, “Principles of Economics”, 3rd ed. (2022), Appendix D “The Expenditure-Output Model”.

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